{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:RC6BNNTZREOUCISXLWQSZPNFGD","short_pith_number":"pith:RC6BNNTZ","canonical_record":{"source":{"id":"1108.2696","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2011-08-12T19:43:05Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"a37479b13ca0528cec89175b174cb76a45b91a4b5aab789439cef44de98bf179","abstract_canon_sha256":"f50af8fdb7f26924c6be639cdb63815ca86a4dfc0a86f5ec35ad5c28b790dcb7"},"schema_version":"1.0"},"canonical_sha256":"88bc16b679891d4122575da12cbda530c6149960644a8771990cc8cf4c2deee3","source":{"kind":"arxiv","id":"1108.2696","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.2696","created_at":"2026-05-18T02:00:54Z"},{"alias_kind":"arxiv_version","alias_value":"1108.2696v1","created_at":"2026-05-18T02:00:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.2696","created_at":"2026-05-18T02:00:54Z"},{"alias_kind":"pith_short_12","alias_value":"RC6BNNTZREOU","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RC6BNNTZREOUCISX","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RC6BNNTZ","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:RC6BNNTZREOUCISXLWQSZPNFGD","target":"record","payload":{"canonical_record":{"source":{"id":"1108.2696","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2011-08-12T19:43:05Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"a37479b13ca0528cec89175b174cb76a45b91a4b5aab789439cef44de98bf179","abstract_canon_sha256":"f50af8fdb7f26924c6be639cdb63815ca86a4dfc0a86f5ec35ad5c28b790dcb7"},"schema_version":"1.0"},"canonical_sha256":"88bc16b679891d4122575da12cbda530c6149960644a8771990cc8cf4c2deee3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:00:54.529228Z","signature_b64":"shCnoYLWYbGzfCCjxofhGdI6rBOHEGDxwaxX0RjTxJnl3/Egi6iudKogSkabL79AC/VtFzKnnCT8rbLoJm67DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"88bc16b679891d4122575da12cbda530c6149960644a8771990cc8cf4c2deee3","last_reissued_at":"2026-05-18T02:00:54.528292Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:00:54.528292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.2696","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:00:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9rXS96C8KxSO0bvBCc8HCZSyry87p9C8kBn9RcP6aWc8XOuvP7GDfcoc+OztOnIaFuX5iYjEMJMq6ya3RPy8Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T16:12:32.226701Z"},"content_sha256":"3d1e2187156907d7f285f676be74f420f12083408fadebfe87defecda99f8f83","schema_version":"1.0","event_id":"sha256:3d1e2187156907d7f285f676be74f420f12083408fadebfe87defecda99f8f83"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:RC6BNNTZREOUCISXLWQSZPNFGD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spatial Structure of Stationary Nonequilibrium States in the Thermostatted Periodic Lorentz Gas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.CD","authors_text":"Alexey Korepanov, Federico Bonetto, Joel L. Lebowitz, Nikolay Chernov","submitted_at":"2011-08-12T19:43:05Z","abstract_excerpt":"We investigate analytically and numerically the spatial structure of the non-equilibrium stationary states (NESS) of a point particle moving in a two dimensional periodic Lorentz gas (Sinai Billiard). The particle is subject to a constant external electric field E as well as a Gaussian thermostat which keeps the speed |v| constant. We show that despite the singular nature of the SRB measure its projections on the space coordinates are absolutely continuous. We further show that these projections satisfy linear response laws for small E. Some of them are computed numerically. We compare these r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2696","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:00:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aeXgiLphX0JNjJgxNFbeQ71C2iP9+RgEhVcbPnZ/Tq/bvB8oPZCMDQab7xlQyS4Ay/neWeNjPqjz7myPnqYBDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T16:12:32.227055Z"},"content_sha256":"dee2eb11961abc4f4f7957aa6e8543b87c7b34bce586b46e53da105cf7a2ef58","schema_version":"1.0","event_id":"sha256:dee2eb11961abc4f4f7957aa6e8543b87c7b34bce586b46e53da105cf7a2ef58"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RC6BNNTZREOUCISXLWQSZPNFGD/bundle.json","state_url":"https://pith.science/pith/RC6BNNTZREOUCISXLWQSZPNFGD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RC6BNNTZREOUCISXLWQSZPNFGD/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-29T16:12:32Z","links":{"resolver":"https://pith.science/pith/RC6BNNTZREOUCISXLWQSZPNFGD","bundle":"https://pith.science/pith/RC6BNNTZREOUCISXLWQSZPNFGD/bundle.json","state":"https://pith.science/pith/RC6BNNTZREOUCISXLWQSZPNFGD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RC6BNNTZREOUCISXLWQSZPNFGD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:RC6BNNTZREOUCISXLWQSZPNFGD","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f50af8fdb7f26924c6be639cdb63815ca86a4dfc0a86f5ec35ad5c28b790dcb7","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2011-08-12T19:43:05Z","title_canon_sha256":"a37479b13ca0528cec89175b174cb76a45b91a4b5aab789439cef44de98bf179"},"schema_version":"1.0","source":{"id":"1108.2696","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.2696","created_at":"2026-05-18T02:00:54Z"},{"alias_kind":"arxiv_version","alias_value":"1108.2696v1","created_at":"2026-05-18T02:00:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.2696","created_at":"2026-05-18T02:00:54Z"},{"alias_kind":"pith_short_12","alias_value":"RC6BNNTZREOU","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RC6BNNTZREOUCISX","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RC6BNNTZ","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:dee2eb11961abc4f4f7957aa6e8543b87c7b34bce586b46e53da105cf7a2ef58","target":"graph","created_at":"2026-05-18T02:00:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We investigate analytically and numerically the spatial structure of the non-equilibrium stationary states (NESS) of a point particle moving in a two dimensional periodic Lorentz gas (Sinai Billiard). The particle is subject to a constant external electric field E as well as a Gaussian thermostat which keeps the speed |v| constant. We show that despite the singular nature of the SRB measure its projections on the space coordinates are absolutely continuous. We further show that these projections satisfy linear response laws for small E. Some of them are computed numerically. We compare these r","authors_text":"Alexey Korepanov, Federico Bonetto, Joel L. Lebowitz, Nikolay Chernov","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2011-08-12T19:43:05Z","title":"Spatial Structure of Stationary Nonequilibrium States in the Thermostatted Periodic Lorentz Gas"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2696","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3d1e2187156907d7f285f676be74f420f12083408fadebfe87defecda99f8f83","target":"record","created_at":"2026-05-18T02:00:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f50af8fdb7f26924c6be639cdb63815ca86a4dfc0a86f5ec35ad5c28b790dcb7","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2011-08-12T19:43:05Z","title_canon_sha256":"a37479b13ca0528cec89175b174cb76a45b91a4b5aab789439cef44de98bf179"},"schema_version":"1.0","source":{"id":"1108.2696","kind":"arxiv","version":1}},"canonical_sha256":"88bc16b679891d4122575da12cbda530c6149960644a8771990cc8cf4c2deee3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"88bc16b679891d4122575da12cbda530c6149960644a8771990cc8cf4c2deee3","first_computed_at":"2026-05-18T02:00:54.528292Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:00:54.528292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"shCnoYLWYbGzfCCjxofhGdI6rBOHEGDxwaxX0RjTxJnl3/Egi6iudKogSkabL79AC/VtFzKnnCT8rbLoJm67DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:00:54.529228Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.2696","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d1e2187156907d7f285f676be74f420f12083408fadebfe87defecda99f8f83","sha256:dee2eb11961abc4f4f7957aa6e8543b87c7b34bce586b46e53da105cf7a2ef58"],"state_sha256":"1bb0964a14177db03f1e32a314018d83c816ca4b2bc8f84e455d67833e71e2d3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2viDeLQlFjQSdAlAYrtIJ5ujupnqQ9U4gR5AT7w+DVICQRRapSXgztMtKMm4VyKP7lfuVUKPBZWD3h7IZ2aWBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T16:12:32.230073Z","bundle_sha256":"38a887f0bce724e456cfcdd1a9a49d3850029460c0c724526fbe28311bdbb237"}}